System and method for defining a drilling path based on cost

ABSTRACT

Provided is a method for selecting one of a plurality of convergence paths that may be drilled by a bottom hole assembly (BHA) comprising identifying, by a computer system, a plurality of geometric convergence paths, wherein each of the geometric convergence paths provides a convergence solution from a defined bottom hole assembly (BHA) location to a target drilling path of a well plan. An offset distance is calculated for drilling by the BHA each of the geometric convergence paths connecting the BHA location to the target drilling path. A drill path curvature associated with drilling each of the geometric convergence paths by the BHA is determined by the computer system. A time required for drilling each of the geometric convergence paths by the BHA is determined by the computer system. An optimal geometric convergence path of the plurality of geometric convergence paths is determined responsive to the offset distance for drilling each of the geometric convergence paths, the drill path curvature associated with each of the geometric convergence paths and the time required for drilling each of the geometric convergence paths. The determined optimal geometric convergence path is fed to a controller associated with a display of a drilling rig and used to control the display of the drilling rig to display the determined optimal geometric convergence path.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.14/660,298, filed Mar. 17, 2015, entitled SYSTEM AND METHOD FORSELECTING A DRILLING PATH BASED ON COST (Atty. Dkt. No. MTDI-33160),which is a continuation of U.S. patent application Ser. No. 14/067,390,filed Oct. 30, 2013, entitled SYSTEM AND METHOD FOR DEFINING A DRILLINGPATH BASED ON COST, now U.S. Pat. No. 8,996,396, issued Mar. 31, 2015(Atty. Dkt. No. HADT-31671), which claims the benefit of U.S.Provisional Application No. 61/839,731, filed Jun. 26, 2013, andentitled SYSTEM AND METHOD FOR SELECTING A DRILLING PATH BASED ON COST(Atty. Dkt. No. HADT-31806), the specifications of which areincorporated herein by reference in their entirety.

TECHNICAL FIELD

The following disclosure relates to directional and conventionaldrilling.

BACKGROUND

Drilling a borehole for the extraction of minerals has become anincreasingly complicated operation due to the increased depth andcomplexity of many boreholes, including the complexity added bydirectional drilling. Drilling is an expensive operation and errors indrilling add to the cost and, in some cases, drilling errors maypermanently lower the output of a well for years into the future.Current technologies and methods do not adequately address thecomplicated nature of drilling. Accordingly, what is needed are a systemand method to improve drilling operations.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding, reference is now made to thefollowing description taken in conjunction with the accompanyingDrawings in which:

FIG. 1 illustrates one embodiment of an environment within which variousaspects of the present disclosure may be implemented;

FIG. 2A illustrates one embodiment of a drilling system that may be usedwithin the environment of FIG. 1;

FIG. 2B illustrates one embodiment of a computer system that may be usedwithin the environment of FIG. 2A;

FIG. 3 illustrates a flow chart of one embodiment of a method that maybe used to select one of a plurality of convergence paths based on cost;

FIG. 4 illustrates a flow chart of one embodiment of a method that maybe used with the method of FIG. 3 to identify the cost of a convergencepath;

FIG. 5A illustrates a flow chart of one embodiment of a method that maybe used with the method of FIG. 4 to identify the offset cost of aconvergence path;

FIGS. 5B-5D illustrate embodiments of a two dimensional diagram of acost curve;

FIG. 6 illustrates a flow chart of one embodiment of a method that maybe used with the method of FIG. 4 to identify the curvature cost of aconvergence path; and

FIGS. 7 and 8 illustrate flow charts of different embodiments of amethod that may be used with the method of FIG. 4 to identify the timecost of a convergence path.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like reference numbers are usedherein to designate like elements throughout, the various views andembodiments of a system and method for selecting a drilling path basedon cost are illustrated and described, and other possible embodimentsare described. The figures are not necessarily drawn to scale, and insome instances the drawings have been exaggerated and/or simplified inplaces for illustrative purposes only. One of ordinary skill in the artwill appreciate the many possible applications and variations based onthe following examples of possible embodiments.

Referring to FIG. 1, one embodiment of an environment 100 is illustratedwith a formation 102. A borehole is to be drilled or is being drilledwithin the formation 102 and there is a target path 104 for theborehole. Calculating paths for a borehole in a formation is a complexand often difficult to understand process that frequently uses acombination of known factors and estimates. Whether calculating the pathprior to the beginning of drilling or attempting to return to a desiredpath when drilling has gone off course, there are an infinite number ofpaths from which to choose. Each of these paths has an associatedfinancial cost that is difficult to identify due to the number offactors involved. However, the financial cost of a path is important tothe business of drilling and needs to be taken into account.Accordingly, by normalizing drilling variables into a monetary unit(e.g., United States dollars) as described in the present disclosure,multiple path options can be evaluated in terms of financial cost andthe path that best satisfies one or more defined cost parameters can beselected.

In the present example, the target path 104 represents an optimal paththat has zero cost and provides maximum value. In other words, followingthe target path 104 has no penalty as there is no “better” way to drillthrough the formation 102 than along the target path 104. It isunderstood that “better” is a relative term that may be based on variousselected factors, imperfect data and/or conclusions, and/or availableequipment, and so may not be the actual best possible path if otherfactors were selected, additional information was known, and/or if otherequipment was available. In terms of cost, the target path 104 has zerocost because there is no penalty for being on target. In other words,while there is a drilling cost associated with the target path 104because the target path 104 cannot be drilled for free, the target path104 is assigned zero cost in the present example because the cost of thetarget path 104 is the baseline cost and only paths that stray from thetarget path 104 will be assigned cost penalties. The target path 104 maybe defined by a well plan, seismic data, and/or any other informationsuitable for delineating the path through the formation 102.

For purposes of example, paths 108, 110, 112, 114, 116, and 118illustrate possible convergence paths from a point 106 representing acurrent or future bottom hole assembly (BHA) location to the target path104. Although not discussed in detail herein, the calculation of theconvergence paths themselves may use any of a number of processes. Onepossible method for such convergence path calculations is disclosed inU.S. application Ser. No. 13/530,298, filed on Jun. 22, 2012, andentitled SYSTEM AND METHOD FOR DETERMINING INCREMENTAL PROGRESSIONBETWEEN SURVEY POINTS WHILE DRILLING, which is hereby incorporated byreference in its entirety.

As will be discussed below, after the paths 108, 110, 112, 114, 116, and118 are calculated, each path may be assigned a cost and then evaluatedbased on that cost relative to the costs of the other paths. Forexample, from a distance perspective, path 108 has a greater length thanpath 116 and much of that length is farther from the target path 104than the length of path 110. In contrast, path 110 narrows the distanceto the target path 104 more rapidly. However, path 110 requires moresliding, which takes time and introduces complexities in steering. Thesefactors and/or others need to be weighed to determine whether theshorter length of path 110 actually results in a lower cost. Paths 108and 116 converge sharply with the target path 104 and it appears likelythat overshoot will occur unless an unrealistic build rate is applied.Path 114 may converge sharply, but does not extend far enough todetermine what will happen. Paths 110, 112, and 118 offer morereasonable convergence angles, although some correction may still needto be made. The paths 108, 110, 112, 114, 116, and 118 offer variousalternatives, each with different curvature, length, offset from thetarget path 104, and time considerations that affect the cost of thatparticular path. To address costs beyond the point of convergence, eachpath may also have an extension cost, which will be discussed in greaterdetail below.

By calculating a monetary value (e.g., a value in United States dollars)for a particular segment of a path (e.g., a unit of measure such as afoot) and adding up all the segments for the path, a cost can beidentified for a particular path. For example, assume that the targetpath has a value of $1000 per foot based on a PV10 value (e.g., thepresent value of estimated future oil and gas revenues, net of estimateddirect expenses, discounted at an annual discount rate of 10%). Thetarget path 104 would be $0 per foot in cost. A cost for a convergencepath can then be calculated for each segment (e.g., foot) of theconvergence path based on the target path's value, and the total cost ofall the segments is the cost of the convergence path.

The process of calculating the cost of a path may involve identifyingany of a number of different types of cost, such as a distance cost, asliding cost, a curvature cost, a time cost, a dogleg cost, a deviationcost, and/or a launch penalty cost. Some of these costs may be used tocalculate other costs. For example, the launch penalty cost may be usedto calculate the curvature cost.

Accordingly, the present disclosure may be used to provide a relativelyeasy to understand picture of which path should be selected from manydifferent possible paths from a cost standpoint. For example, if theborehole is being drilled and the BHA is off of the target path, a costcomparison may be used to determine the best convergence path in termsof cost for returning the BHA to the target path when there are aninfinite number of paths from which to choose. As the best convergencepath may not be the shortest or most direct path, using a cost basedselection analysis enables drilling decisions to be based on maximizingvalue and minimizing cost.

Although FIG. 1 is a two-dimensional drawing, it is understood that thevarious paths illustrated in FIG. 1 may be three-dimensional in nature.Furthermore, it is understood that although various lines areillustrated as straight lines for purposes of clarity (e.g., the targetpath 104), such lines need not be straight. Furthermore, although shownas lines, it is understood that paths may be zones. For example, thetarget path 104 may be a three dimensional zone and drilling inside thezone may be assigned zero cost.

Referring to FIG. 2A, one embodiment of a drilling environment 200 isillustrated that may be used within the environment of FIG. 1. Althoughthe environment 200 is a drilling environment that is described with atop drive drilling system, it is understood that other embodiments mayinclude other drilling systems, such as rotary table systems.

In the present example, the environment 200 includes a derrick 202 on asurface 203. The derrick 202 includes a crown block 204. A travelingblock 206 is coupled to the crown block 204 via a drilling line 208. Ina top drive system (as illustrated), a top drive 210 is coupled to thetraveling block 206 and provides the rotational force needed fordrilling. A saver sub 212 may sit between the top drive 210 and a drillpipe 214 that is part of a drill string 216. The top drive 210 rotatesthe drill string 216 via the saver sub 212, which in turn rotates adrill bit 218 of a BHA 220 in a borehole 222 in the formation 102. A mudpump 224 may direct a fluid mixture (e.g., mud) 226 from a mud pit orother container 228 into the borehole 222. The mud 226 may flow from themud pump 224 into a discharge line 230 that is coupled to a rotary hose232 by a standpipe 234. The rotary hose 232 is coupled to the top drive210, which includes a passage for the mud 226 to flow into the drillstring 216 and the borehole 222. A rotary table 236 may be fitted with amaster bushing 238 to hold the drill string 216 when the drill string isnot rotating.

Some or all of a control system 242 may be located at the derrick 202,may be downhole, and/or may be remote from the actual drilling location.For example, the control system 242 may be a system such as is disclosedin U.S. Pat. No. 8,210,283 entitled SYSTEM AND METHOD FOR SURFACESTEERABLE DRILLING, filed on Dec. 22, 2011, and issued on Jul. 3, 2012,which is hereby incorporated by reference in its entirety.Alternatively, the control system 242 may be a standalone system or maybe incorporated into other systems at the derrick 202. The controlsystem 242 may communicate via a wired and/or wireless connection (notshown).

Referring to FIG. 2B, one embodiment of a computer system 250 isillustrated. The computer system 250 is one possible example of a systemcomponent or device such as the control system 242 of FIG. 2A or aseparate system used to perform the various processes described herein.In scenarios where the computer system 250 is on-site, such as withinthe environment 100 of FIG. 1, the computer system may be contained in arelatively rugged, shock-resistant case that is hardened for industrialapplications and harsh environments. It is understood that downholeelectronics may be mounted in an adaptive suspension system that usesactive dampening as described in various embodiments herein.

The computer system 250 may include a central processing unit (“CPU”)252, a memory unit 254, an input/output (“I/O”) device 256, and anetwork interface 258. The components 252, 254, 256, and 258 areinterconnected by a transport system (e.g., a bus) 260. A power supply(PS) 262 may provide power to components of the computer system 250 viaa power transport system 264 (shown with data transport system 260,although the power and data transport systems may be separate).

It is understood that the computer system 250 may be differentlyconfigured and that each of the listed components may actually representseveral different components. For example, the CPU 252 may actuallyrepresent a multi-processor or a distributed processing system; thememory unit 254 may include different levels of cache memory, mainmemory, hard disks, and remote storage locations; the I/O device 256 mayinclude monitors, keyboards, and the like; and the network interface 258may include one or more network cards providing one or more wired and/orwireless connections to a network 266. Therefore, a wide range offlexibility is anticipated in the configuration of the computer system250.

The computer system 250 may use any operating system (or multipleoperating systems), including various versions of operating systemsprovided by Microsoft (such as WINDOWS), Apple (such as Mac OS X), UNIX,and LINUX, and may include operating systems specifically developed forhandheld devices, personal computers, and servers depending on the useof the computer system 250. The operating system, as well as otherinstructions (e.g., software instructions for performing thefunctionality described in previous embodiments) may be stored in thememory unit 254 and executed by the processor 252. For example, thememory unit 254 may include instructions for performing the variousmethods and control functions disclosed herein.

The network 266 may be a single network or may represent multiplenetworks, including networks of different types. For example, thenetwork 266 may include one or more cellular links, data packet networkssuch as the Internet, local area networks (LANs), and/or wide local areanetworks (WLAN), and/or Public Switched Telephone Networks (PSTNs).Accordingly, many different network types and configurations may be usedto couple the computer system 250 to other components of the environment200 of FIG. 2A and/or to other systems not shown (e.g., remote systems).

Referring to FIG. 3, one embodiment of a method 300 illustrates aprocess that may be used to select a convergence path from multiplepossible convergence paths when a BHA (e.g., the BHA 220 of FIG. 2A) isoff a target path (e.g., the target path 104 of FIG. 1). In the threedimensional space of a formation (e.g., the formation 102 of FIG. 1),there may be an infinite number of possible convergence paths. Themethod 300 may be used to identify multiple possible convergence paths,narrow the identified paths to a single “best” path based on cost, andselect that path as the path to be used.

It is understood that “best” is a relative term that may be based on oneor more parameters, and so may not be the best path if other parametersare selected. In the present example, the best path is the lowest costpath in terms of a monetary unit, but it is understood that the bestpath may be otherwise defined. For example, in some embodiments, thebest path may be the second to lowest cost path or may be the lowestcost path based on a particular cost parameter (e.g., time cost).Accordingly, while the best path is the path with the lowest overallcost for purposes of example, other best paths may exist and may beselected based on the particular needs for a path.

In step 302, drilling plan information is obtained for convergencesolution calculations if it has not already been obtained. The drillingplan information may be a well plan, seismic data, and/or any otherinformation that defines the target path 104 that the BHA 220 is tofollow. Current BHA information such as location, trajectory, ROP, andother information may also be obtained so that a convergence plan can becalculated to realign the BHA with the target path 104. Otherinformation, such as drift information, may be obtained if not includedin the drilling plan information for use in sliding and/or rotationcalculations.

In step 304, multiple geometric paths are calculated. The number ofgeometric paths that are calculated may depend on factors such asavailable processing power and/or the number and/or values of selectedparameters (e.g., parameters may be selected to constrain the number ofgeometric paths). For example, parameters may limit the minimum and/ormaximum length of a path, the maximum allowable dogleg severity, thedirection, the inclination, and/or other path variables. The totalnumber of paths may be limited by selecting appropriate parameters andparameter values. For purposes of example, 500,000 paths may becalculated, but it is understood that fewer or more (e.g., one millionor more) paths may be calculated in other embodiments.

In step 306, the geometric paths are pruned to remove illogical options.For example, while geometrically possible, some paths may go in thewrong direction at some point and yet still converge. These paths can beeliminated as they are not likely to be the lowest cost solution. Insome embodiments, step 306 may be handled as parameters used in step 304(e.g., parameters may be selected that remove the possibility ofcalculating paths that go in the wrong direction). The pruning of step306 reduces the number of paths for which later calculations are needed.This may speed up calculations, thereby providing a performance benefit.

In step 308, the paths remaining after the pruning of step 306 arepassed through a rule set and paths violating the rules are removed fromconsideration. For example, one or more rules may define a threshold formaximum allowable dogleg severity. Any paths that have doglegs above thethreshold may be discarded. One or more other rules may define athreshold for a maximum allowable curvature for the entire path and anypaths having an overall curvature above the threshold may be discarded.The rule set may be used to provide a relatively fine level of controland/or may be used to test different outcomes without having to redo thepruning of step 306.

It is understood that the method 300 may handle steps 304, 306, and 308in different ways depending on how the method 300 is implemented, andthat steps 304, 306, and/or 308 may overlap or be combined in someembodiments. For example, as described previously, parameters may beused in step 304 to constrain the identification of the geometricconvergence paths. Accordingly, the pruning of step 306 and rule setapplication of step 308 may vary depending on the functionality providedby step 304. Generally, steps 306 and/or 308 provide the ability torefine the selection process for deciding which geometric convergencepaths are to be passed on for cost analysis.

In step 310, a cost may be identified for each path remaining after step308. As will be described later in greater detail, the cost of a pathmay be dependent on various factors such as an offset cost thatpenalizes a path based on distance from the target path, a curvaturecost that penalizes a path for the path's curvature (which has an impacton friction), and/or a time cost that penalizes a path based on theamount of time the path will take. For purposes of example, all three ofthese costs are used to calculate the total cost for a path, but it isunderstood that fewer factors may be used in some embodiments, and thatmore factors may be used in other embodiments.

In step 312, the paths are compared based on cost and, in step 314, thepath that best meets one or more defined cost parameters is selected.For example, the lowest cost path may be selected. In step 316, theselected path is output. Although not shown in FIG. 3, the output may beused to provide drilling instructions for directing the BHA back to thetarget path. For example, the output may be used with the control systemdescribed in previously incorporated U.S. Pat. No. 8,210,283 (SYSTEM ANDMETHOD FOR SURFACE STEERABLE DRILLING) to provide or otherwise form thebasis for drilling instructions.

It is understood that various steps may be added or removed from FIG. 3.For example, in some embodiments, the method 300 may import previouslycalculated geometric convergence paths (removing the need for steps 302and 304). In other embodiments, those imported paths may have alreadybeen pruned (removing the need for step 306) and/or passed through therule set (removing the need for step 308).

Referring to FIG. 4, one embodiment of a method 400 illustrates aprocess that may be used to identify the cost of multiple convergencepaths and then select one of the paths. In the present example, the costof a path is based on the offset cost, the curvature cost, and the timecost as described above.

In step 402, the cost for a convergence path is identified. Morespecifically, the offset cost is identified in step 404, the curvaturecost is identified in step 406, and the time cost is identified in step408. It is understood that identifying the offset cost, the curvaturecost, and the time cost may involve two or more calculations for eachcost. For example, the offset cost, the curvature cost, and/or the timecost may be identified from both an azimuth perspective and a truevertical depth (TVD) perspective. These two dimensional costs may thenbe added together to identify a single offset cost. In otherembodiments, three dimensional calculations may be used to determine theoffset cost. Examples of steps 404, 406, and 408 are described ingreater detail below. In step 410, the outputs of steps 404, 406, and408 are combined to identify the total cost for the path.

In step 412, a determination may be made as to whether the cost ofanother path is to be identified. If the cost of another path is to beidentified, the method 400 returns to step 402 and calculates the costof the next path. If no path remains for which the cost is to becalculated, the method 400 continues to step 414, where the paths arenormalized.

Normalization may be performed because the paths may not be the samelength due to factors such as differences in the timing and length ofrotation and sliding segments. The present embodiment may userotate/slide pairs for purposes of calculations, although each pair mayhave a zero factor where there is either zero rotation or zero sliding.This means that two rotations or two slides may be chained togetherdirectly if the intervening segment is zero. The present embodiment mayhave minimum and maximum path lengths defined for the geometric searchengine and a path may not stop on convergence. It is understood thatconvergence does not necessarily mean that the path actually merges withthe target path 104.

Not stopping on convergence means that the path may continue afterconvergence, which extends the length of the path. This extension has acost that may be calculated separately from the path cost and may beused in comparing paths to identify the least cost path. For example,referring to FIG. 1, each path 108, 110, 112, 114, 116, and 118 isextended past the planned convergence path. As discussed previously,paths 108 and 118 converge sharply (e.g., aggressively) with the targetpath 104, while paths 110, 112, and 118 offer more reasonable (e.g.,less aggressive) convergence angles, although some correction may stillneed to be made.

Accordingly, by extending the paths past convergence, paths with higherbackend loaded costs may be identified. For example, path 108 may need asignificant amount of correction to deal with the amount of overshootcaused by the aggressive convergence angle, while path 118 needs muchless correction. By calculating the extension cost as well as the pathcost, a more complete cost picture can be formed.

A path may be defined in terms of vertical zones, build zones, andlateral zones, with each zone having its own set of rules. For example,a build zone may have a maximum allowed curvature of fourteen degrees,while a lateral zone may have a maximum allowed curvature of fourdegrees. Due to geological factors such as drift, drilling a path as astraight line may not actually result in a straight line becauserotational drilling has a tendency to curve due to drift. Whenformulating and reviewing plans, the geological drift may be accountedfor by drilling somewhat off course relative to a straight line pathand/or by planning corrective slides. Drifting may impose a cost when itcauses undesirable deviations from the plan and may also require a costfor any corrections needed to account for the drift. Furthermore, a pathmay use geological drift (if present in the formation) to account forsliding time and other corrective measures (e.g., may allow the drift tocorrect the course instead of performing a slide). However, if theamount of drift results in a course correction that is too slow and/oroccurs over too great a distance, the drift correction may not occurfast enough to negate the offset cost.

Accordingly, to balance these and other factors, the paths may useempirical geo-drift, ROP, and build rates (e.g., motor yields) tocalculate convergence. Due to the many different factors present in apath (e.g., amount of progress made by a path), paths of differentlengths (e.g., a three hundred foot path versus a four hundred footpath) may be normalized prior to comparison. For example, one path maybe more expensive than another path, but the more expensive path mayhave made an additional fifty feet of progress compared to the cheaperpath. This additional fifty feet of progress has positive value in termsof cost that is not taken into account if the paths are not normalized.This is illustrated in FIG. 1 with respect to paths 108 and 118, forexample, with path 108 converging at a point farther down the targetpath 104 than the point at which path 118 converges.

In the present example, the normalization process is performed bynormalizing all paths against the longest path as follows: (cost of pathbeing normalized/length of path being normalized)*length of longestpath. For example, if the longest path is four hundred feet long and thepath being normalized is two hundred feet long and costs $75,000, thenormalization would result in (($75,000/200)*400=$150,000). The totalcost of the two hundred foot path used for comparison purposes would be$150,000, instead of the actual $75,000 cost. The four hundred foot planwill more expensive if its cost is greater than $150,000, and lessexpensive if its cost is less than $150,000. Accordingly, a cost of$125,000 for the four hundred foot path would make the four hundred footpath more expensive than the two hundred foot path prior tonormalization, but less expensive after normalization is performed.

In step 416, following normalization, the path best meeting the costparameter(s) is identified. For example, the lowest cost path may beidentified. In step 418, the identified path is output. It is understoodthat steps 416 and 418 may be similar or identical to steps 316 and 318of FIG. 3, but are included for purposes of better illustrating theoverall process of FIG. 4. However, a path will generally be selected asingle time (e.g., in one of steps 316 or 416) and output a single time(e.g., in one of steps 318 or 418), and so such duplicate steps may beomitted in an actual implementation of FIG. 3 and FIG. 4. For example,if steps 316 and 318 are implemented, step 416 may be omitted and step418 may be used to output the normalized paths to step 316 forselection.

Referring to FIG. 5A, one embodiment of a method 500 illustrates aprocess that may be used as step 404 of FIG. 4 to identify the offsetcost of a convergence path. It is understood that this is only anexample of step 404 and other methods may be used.

In step 502, the length of a path segment is identified. For purposes ofexample, a segment is one foot in length, but it is understood that asegment may be defined in many different ways. For example, a segmentmay be defined as a distance (e.g., inches, centimeters, yards, ormeters) or may be defined using one or more other measurement criteria(e.g., a length of pipe or a fraction of that length). In step 504, thepath is divided into segments of the identified length. For example, afour hundred foot path would be divided into four hundred segments thatare each one foot in length.

In step 506, a single path segment is identified for cost calculationpurposes. The present step identifies which one of the segments is tohave its cost calculated in this iteration of the method 500. In step508, the segment's distance from the target path is identified. In step510, the segment's location on a cost curve is calculated based ondistance. As described previously, this location identifies the penaltythat is to be applied to the segment, with the penalty generallyincreasing the farther the location is from the target path.

With additional reference to FIGS. 5B-D, various embodiments of a costcurve 530 are illustrated using two-dimensional diagrams. The cost curve530 may show costs, including non-linear and/or non-symmetrical costs,against an axis 532 representing true vertical depth (TVD) and an axis534 representing azimuth. As shown, the diagrams 530 may provide aregion 536 of potential non-linear path costs surrounded by a boundary538 that represents an outer limit of the non-linear costs. It isunderstood that costs may increase outside the boundary 538, but may belinear or non-linear. Without such cost increases outside the boundary,a potential solution that passes the boundary would incur no additionalcost and there would be no cost pressure to return the solution to theregion 536.

The region 536 may include colored and/or otherwise differentiated areasto indicate costs. For example, green (the center portion of the region536 indicated by horizontal lines) yellow (the intermediate portion ofthe region 536 indicated by “+” signs), and red (the outer portion ofthe region 536 indicated by vertical lines) may be used to indicateareas of desirable, borderline, and undesirable costs, respectively.Shading or other indicia may be used to indicate graduated costs, suchas going from a lighter red to a darker red. In addition, it isunderstood that the colors may not be separated by a clear line, but mayfade into one another. For example, green may fade into yellow toindicate that costs are increasing, rather than having an abrupttransition from green to yellow.

In the present embodiment, the cost curve 530 may be manipulated alongone or both axes 532 and 534 by modifying the location of lines 540 and542. One or both of the lines 540 and 542 may be non-linear and/ornon-symmetrical. Manipulation of the lines 540 and 542 may affect theregion 536 (e.g., may shift the costs and therefore the coloration ofthe region) and/or the boundary 538 (e.g., may shift maximum costslimits).

For example, line 540 may be manipulated by moving points 544 and/or546, which may be moved relative to a cost axis 548 and a distance axis550. The points 544 and/or 546 represent the maximum cost penalty withinthe boundary 538. For purposes of illustration, the point 544 may bemoved to a position 552 (FIG. 5D) and the point 546 may be moved to aposition 554 (FIG. 5C). A portion of the line 540 is currently atposition 556 and may be moved, for example, to a position 558 or aposition 560.

Similarly, line 542 may be manipulated by moving points 562 and/or 564,which may be moved relative to a cost axis 566 and a distance axis 568.The points 544 and/or 546 represent the maximum cost penalty within theboundary 538. For purposes of illustration, the point 562 may be movedto a position 570 and the point 564 may be moved to a position 572. Aportion of the line 542 is currently at position 574 and may be moved,for example, to a position 576 or a position 578.

In some embodiments, the cost curve 530 may be provided as a graphicaltool that enables a user to manipulate the lines 540 and 542 for spatialcost assessment when determining a convergence solution. For example, acomputer system (e.g., the computer system 250 of FIG. 2B) may executeone or more of the methods described herein based on the actions of ageologist who is manipulating the lines 540 and 542 via a graphical userinterface. Accordingly, the geologist or other user may “drive” the BHAalong a desirable path as the diagram 530 may be viewed from theperspective of the drill bit/BHA looking forward into the formation froma cost perspective. The computer system may then create a convergenceplan based on how the drill bit/BHA is driven. This allows the geologistto interact visually with the described methods to create a convergenceplan.

In some embodiments, areas (not shown) of extreme or even infinite costmay be defined within the region 536 to prevent solutions from enteringthose areas. For example, a property line that marks a drilling limitmay be given an extreme or infinite cost with the cost rising sharply asthe property line is approached. In another example, an old well may beavoided by marking it as an area of extreme or infinite cost, therebyusing cost as an anti-collision measure. Accordingly, the behavior ofsolutions can be affected by defining geographic zones as areas ofextreme or infinite cost and/or by controlling the rate at which thecosts increase as those zones are approached.

Referring again to FIG. 5A, in step 512, the segment's cost iscalculated based on the cost assigned to the segment's location on thecost curve. Continuing the previous example of the target path 104having a value of $1000 per foot, if the segment is at the $600 mark onthe cost curve, the offset cost is $400 (i.e., $1000−$400=$600) if thecost curve is defined in terms of value. If the cost curve is defined interms of cost, the mark would indicate the $400 cost (e.g., the markidentifies the cost rather than the value). In step 514, the segment'scost is added to the path's cost (e.g., current segment cost+currentpath cost=new path cost).

In step 516, a determination may be made as to whether the cost ofanother segment of the path is to be determined. If the cost of anothersegment is to be identified, the method 500 returns to step 506 andbegins calculating the next segment's cost. If there are no othersegments for which cost is to be identified, the method 500 continues tostep 518. In step 518, the path cost is output.

With additional reference to FIG. 6, one embodiment of a method 600illustrates a process that may be used as step 406 of FIG. 4 to identifythe curvature cost of a convergence path. It is understood that this isonly an example of step 406 and other methods may be used. The curvaturecost addresses the costs associated with curves in the path. Such costsinclude reaming, casing requirements, the impact of friction on laterwell segments, and similar costs. The curvature cost may be viewed as amixture of friction impact, steerage issues, and launch penalty.

The launch penalty can be in a relative zone or an absolute zone andaddresses system stability. The absolute zone launch penalty addressesdrilling above a certain angle (e.g., ninety-eight degrees). This is acommon problem when drilling a horizontal well because moving above thatangle makes it very difficult to get the well to come back down to thedesired path because there is less weight pulling the BHA down (e.g.,gravity is not aiding the course correction as much). Once this tippingpoint angle is reached, the BHA tends to move aggressively away from theplan (e.g., launches).

The relative zone launch penalty addresses the impact of geo-drift anddrilling at an offset from a planned angle. When not staying on bed dip(e.g., when crossing the grain), off course movement may be accelerated.Due to this, drilling against the grain of the formation tends to createan unstable system.

The launch penalty creates an exponential cost curve as the tippingpoint angle is approached and passed or when cross grain drilling isneeded (particularly for an extended period of time) because of thedifficulty in correcting the associated problems. Accordingly, thepresent process applies a launch penalty for approaching angles ordrilling patterns where this aggressive movement may begin. Because thelaunch penalty is an exponential cost curve that penalizes paths thatapproach undesirable situations, the cost increases exponentially thecloser the path gets to the absolute or relative zones.

In step 602, rotation/sliding segments of the path may be identified.This may include identifying the lengths and locations of the rotationsegments and the lengths, locations, and build rates of the slidingsegments. Launch penalty costs may be applied based on build rateinformation. In step 604, the overall curvature of the path isidentified.

In step 606, the peak curvature of the path is identified. The peakcurvature is identified using a defined window (e.g., a window spanninga defined number of feet) to identify dogleg severity. As this window ismoved along the path, the peak curvature is located and generally occurswhen the entire window contains a slide or when the window overlapsmultiple slides. It is understood that the distance defined for thewindow may greatly impact the identified peak curvature. For example,assume there is a five degree curve that occurs within ten feet andthere is not another curve within one hundred feet. Using a slidingwindow spanning one hundred feet will result in a dogleg severity of5°/100 ft. Using a sliding window spanning ten feet will result in adogleg severity of 5°/10 ft, which appears to be a much more severedogleg even though it is actually the same one. The peak curvature,which may be less than the threshold for dogleg severity as applied bythe rules in step 308 of FIG. 3, may be identified to determine costbecause the greater the peak curvature, the greater the impact on laterportions of the path.

For this reason, the locations of curvature may also be identified. Forexample, a curve early in the well will affect the remainder of thewell, while a curve near the end of the well will have far less impacton the path as a well. Accordingly, a curve early in the well may moredrastically affect the cost of the remainder of the well and so may beassigned a higher cost than a curve near the end of the well. Asdescribed above, how the sample size is defined (e.g., the distancespanned by the window), may have a significant impact on how a curve isevaluated.

In step 608, a curvature cost for the path is identified based on theoverall (e.g., average) curvature, peak curvature, and location(s) ofcurvature. In step 610, the curvature cost is output.

Referring to FIG. 7, one embodiment of a method 700 illustrates aprocess that may be used as step 408 of FIG. 4 to identify the time costof a convergence path. It is understood that this is only an example ofstep 408 and other methods may be used.

In step 702, rotation/sliding segments of the path may be identified.This may include identifying the length of the rotation segments and thelength and build rate of the sliding segments. In some embodiments, thismay use information from step 602 of FIG. 6 or information from thisstep of the method 700 may be used with the method 600 of FIG. 6. Instep 704, a time for each segment may be identified. For example, thereis an ROP for sliding and an ROP for rotating, and one or both of theseROPs may change over time. In addition, there may be a setup time neededto prepare for a slide, which may include the time needed to orient thetoolface and account for reactional torque in preparation for the slide.Accordingly, the total time may be calculated as ((ROP for slide*slidedistance)+(ROP for rotation*rotation distance)+setup time for slide).

Empirical ROP information may be used to provide current time data.Generally, sliding segments will have higher time costs than rotationsegments of the same length and the ROP and/or time may change dependingon the bit's location in the well. There is a ratio of slide ROP versusrotation ROP and this ratio may change over the course of the well. Forexample, in the vertical portion of the well, the slide/rotation ROP maybe a 4:1 ratio, while at the end of the lateral it may be a 20:1 ratio.This is empirically calculated in real time or near real time so thatthe cost penalty threshold may be continuously updated. Accordingly, thepenalty for sliding at the end of the well may be different than thepenalty for sliding at the beginning of the well and the method 700 maytake this into account using the empirically calculated ROP.

In step 706, the total time for the path may be identified. This mayinclude adding together the times calculated in step 704 or may includeother calculations. In step 708, a time cost is calculated for the pathbased on the cost of the rig per unit time (e.g., total path time*rigcost per unit time=path cost). Rig time may include some or all costsassociated with the rig, including labor costs, operating costs (e.g.,fuel), material costs (e.g., pipe), and/or other costs. For example,assume that a slide segment has a setup time of ten minutes and a slidetime of forty minutes, and the rig has a time cost of $75,000 per day.The segment cost would be fifty minutes times the rig cost per minute(e.g., 50 minutes*($75,000/1440 minutes)=$2604.17). This could furtherbe divided into cost per foot and/or otherwise converted for additionalcomparisons and/or calculations. In step 710, the time cost is output.

Referring to FIG. 8, one embodiment of a method 800 illustrates anotherprocess that may be used as step 408 of FIG. 4 to identify the time costof a convergence path. It is understood that this is only an example ofstep 408 and other methods may be used. As shown in FIG. 8, cost may becalculated per segment in step 806 and the segment costs may be added toidentify the total path cost in step 808. As the steps are similar oridentical to those of FIG. 7 with the exception of steps 806 and 808,FIG. 8 is not described in additional detail herein.

It will be appreciated by those skilled in the art having the benefit ofthis disclosure that this system and method for selecting a drillingpath based on cost provides an improved process for comparing drillingpaths on a cost basis and selecting the drilling path that bestsatisfies one or more cost parameters. It should be understood that thedrawings and detailed description herein are to be regarded in anillustrative rather than a restrictive manner, and are not intended tobe limiting to the particular forms and examples disclosed. On thecontrary, included are any further modifications, changes,rearrangements, substitutions, alternatives, design choices, andembodiments apparent to those of ordinary skill in the art, withoutdeparting from the spirit and scope hereof, as defined by the followingclaims. Thus, it is intended that the following claims be interpreted toembrace all such further modifications, changes, rearrangements,substitutions, alternatives, design choices, and embodiments.

What is claimed is:
 1. A method for selecting one of a plurality ofconvergence paths that may be drilled by a bottom hole assembly (BHA)comprising: identifying, by a computer system, a plurality of geometricconvergence paths, wherein each of the geometric convergence pathsprovides a convergence solution from a defined bottom hole assembly(BHA) location to a target drilling path of a well plan; calculating, bythe computer system, an offset distance for drilling by the BHA each ofthe geometric convergence paths connecting the BHA location to thetarget drilling path; determining, by the computer system, a drill pathcurvature associated with drilling each of the geometric convergencepaths by the BHA; determining, by the computer system, a time requiredfor drilling each of the geometric convergence paths by the BHA;determining, by the computer system, an optimal geometric convergencepath of the plurality of geometric convergence paths responsive to theoffset distance for drilling each of the geometric convergence paths,the drill path curvature associated with each of the geometricconvergence paths and the time required for drilling each of thegeometric convergence paths; feeding the determined optimal geometricconvergence path to a controller associated with a display of a drillingrig; controlling, by the controller, the display of the drilling rig todisplay the determined optimal geometric convergence path.
 2. The methodof claim 1, wherein the step of identifying further comprises:obtaining, by the computer system, drill plan information relating to awell plan; and identifying, by the computer system, the plurality ofgeometric convergence paths responsive to the drill plane information.3. The method of claim 2, wherein the drill plan information comprisesat least one of the well plan, seismic data, data defining the targetpath, BHA location, BHA trajectory, BHA ROP and drift information
 4. Themethod of claim 2, wherein the step of identifying further compriseslimiting the plurality of convergence paths to a predetermined number ofconvergence paths.
 5. The method of claim 2, wherein the step ofidentifying further comprises the steps of removing some of theplurality of convergence paths to remove illogical convergence paths. 6.The method of claim 2, wherein the step of identifying further comprisescomparing the plurality of convergence paths to a predetermined rule setto remove a portion of the plurality of convergence paths from furtherconsideration for violating rules of the predetermined rule set.
 7. Themethod of claim 1, wherein the step of determining the optimal geometricconvergence path is further responsive to geometric drift associatedwith the plurality of convergence paths.
 8. The method of claim 1,wherein the step of determining the optimal geometric convergence pathfurther comprises normalizing each of the plurality of convergence pathsagainst a longest convergence path.
 9. The method of claim 1, whereinthe step of calculating the offset distance for each of the plurality ofgeometric convergence paths further comprises calculating the offsetdistance for a plurality of segments making up a geometric convergencepath of the plurality of geometric convergence paths.
 10. The method ofclaim 1, wherein the step of determining a drill path curvature furthercomprises the step of determining, by the computer system a peak drillpath curvature associate with drilling each of the plurality ofgeometric convergence paths.
 11. The method of claim 1, wherein the stepof determining the time required for drilling each of the plurality ofgeometric convergence paths further comprise determining a time requiredto for drilling a plurality of segments making up a convergence path ofthe plurality of geometric convergence paths.
 12. The method of claim 1,wherein the step of determining the time required for drilling each ofthe plurality of geometric convergence paths is further responsive to arate of penetration (ROP) for slide, a slide distance, an ROP forrotation, a rotation distance and a setup time for the slide.
 13. Amethod for selecting one of a plurality of convergence paths that may bedrilled by a bottom hole assembly (BHA) comprising: identifying, by acomputer system, a plurality of geometric convergence paths, whereineach of the geometric convergence paths provides a convergence solutionfrom a defined bottom hole assembly (BHA) location to a target drillingpath of a well plan; calculating, by the computer system, an offsetdistance for drilling by the BHA each of the geometric convergence pathsconnecting the BHA location to the target drilling path; determining, bythe computer system, a drill path curvature associated with drillingeach of the geometric convergence paths by the BHA; determining, by thecomputer system, a time required for drilling each of the geometricconvergence paths by the BHA; determining, by the computer system, anoptimal geometric convergence path of the plurality of geometricconvergence paths responsive to at least one of the offset distance fordrilling each of the geometric convergence paths, the drill pathcurvature associated with each of the geometric convergence paths andthe time required for drilling each of the geometric convergence paths;feeding the determined optimal geometric convergence path to acontroller associated with a display of a drilling rig; controlling, bythe controller, the display of the drilling rig to display thedetermined optimal geometric convergence path.
 14. The method of claim13, wherein the step of identifying further comprises: obtaining, by thecomputer system, drill plan information relating to a well plan; andidentifying, by the computer system, the plurality of geometricconvergence paths responsive to the drill plane information.
 15. Themethod of claim 14, wherein the drill plan information comprises atleast one of the well plan, seismic data, data defining the target path,BHA location, BHA trajectory, BHA ROP and drift information
 16. Themethod of claim 14, wherein the step of identifying further compriseslimiting the plurality of convergence paths to a predetermined number ofconvergence paths.
 17. The method of claim 14, wherein the step ofidentifying further comprises the steps of removing some of theplurality of convergence paths to remove illogical convergence paths.18. The method of claim 14, wherein the step of identifying furthercomprises comparing the plurality of convergence paths to apredetermined rule set to remove a portion of the plurality ofconvergence paths from further consideration for violating rules of thepredetermined rule set.
 19. The method of claim 13, wherein the step ofdetermining the optimal geometric convergence path is further responsiveto geometric drift associated with the plurality of convergence paths.20. The method of claim 13, wherein the step of determining the optimalgeometric convergence path further comprises normalizing each of theplurality of convergence paths against a longest convergence path. 21.The method of claim 13, wherein the step of calculating the offsetdistance for each of the plurality of geometric convergence pathsfurther comprises calculating the offset distance for a plurality ofsegments making up a geometric convergence path of the plurality ofgeometric convergence paths.
 22. The method of claim 13, wherein thestep of determining a drill path curvature further comprises the step ofdetermining, by the computer system a peak drill path curvatureassociate with drilling each of the plurality of geometric convergencepaths.
 23. The method of claim 13, wherein the step of determining thetime required for drilling each of the plurality of geometricconvergence paths further comprise determining a time required to fordrilling a plurality of segments making up a convergence path of theplurality of geometric convergence paths.
 24. The method of claim 13,wherein the step of determining the time required for drilling each ofthe plurality of geometric convergence paths is further responsive to arate of penetration (ROP) for slide, a slide distance, an ROP forrotation, a rotation distance and a setup time for the slide.